Problem: ${11 \div \dfrac{3}{4} =}$
${11} \div \dfrac{3}{4}} ={\dfrac{11}{1}} \div \dfrac{3}{4}} $ $~~~~~~~{\gray{\text{Rewrite 11 as }\dfrac{11}{1}}}. $ $\phantom{11 \div \dfrac{2}{3}}} ={\dfrac{11}{1}} \times \dfrac{4}{3}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac{3}{4}.}} $ $\phantom{11 \div \dfrac{2}{3}}} ={\dfrac{{11}\times4}}{1\timesD3}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{44}{3}} $ ${11 \div \dfrac{3}{4} =\dfrac{44}{3}}$ [Wait, can we rewrite the answer as a mixed number?]